MASS ACTION LAW AND MINORITY CARRIER CONCENTRATION ~ ECE

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Thursday, 14 February 2013

MASS ACTION LAW AND MINORITY CARRIER CONCENTRATION

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MASS ACTION LAW

Under thermal equilibrium the product of the free electron concentration $n$ and the free hole concentration $p$ is equal to a constant equal to the square of intrinsic carrier concentration $n_{i}$ . The intrinsic carrier concentration is a function of temperature.

The equation for the mass action law for semiconductors is

$np = n_{i}^{2}$

PRINCIPLE OF ELECTRICAL NEUTRALITY

it states that

N_D + p = N_A + n

N_D = donor concentration

N_A = acceptor concentration

p = hole concentration

n = electron concentration

Derivations

case - 1 Intrinsic semiconductor ( N_D = N_A = 0 since no impurities )

By the law neutrality

p = n

by mass action law

$np = n_{i}^{2}$

p² = n²= n_i²

p =n = n_i

CASE - 2 n-type ( N_A = 0 )

Let p_n be the intrinsic hole concentration and n_n be the intrinsic electron concentration in n-type

By law of neutrality

N_D + p_n = N_A +n_n

N_D approximately equal to n_n because donor concentration is very much greater than intrinsic hole concentration

By mass action law

p_nn_n = n_i²

p_n= n_i² /n_n = n_i² /N_D

CASE -3 p-type ( N_D = 0 )

Let p_p be the intrinsic hole concentration and n_p be the intrinsic electron concentration in p-type

By law of neutrality

N_D + p_p = N_A +n_p

N_Aapproximately equal to pp because acceptor concentration is very much greater than intrinsic electron concentration.

By mass action law

P_pn_p= n_i²

n_p= n_i² /p_p = n_i² /N_A

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